Waste-disposal systems having tube-dispensing units or refills are commonly used, for numerous reasons. One of the reasons is that such systems often have mechanisms to retain odors. Also, such waste-disposal systems are made to limit the manipulations of bags, to avoid hand contamination. However, any configuration ensuring that the tube-dispensing units are correctly installed in the bins, and that the tube-dispensing unit remains in place in the waste-disposal bin, are desirable. By having the tube-dispensing units correctly installed in the bins, one ensures that the bag is properly sealed and that the risk of hand contamination is minimized.